19.03.2023 - 16:10

The state of Michigan has just changed one of its toll roads from the human collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more smoothly through the toll plaza. With human attendants, the mean number of

The state of Michigan has just changed one of its toll roads from the human collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more smoothly through the toll plaza. With human attendants, the mean number of cars passing through the toll plaza was 1,253 per hour. A random sample of 100 hours under the new machine system of toll collection shows a mean of 1,261, with a standard deviation of 59. Present a hypothesis and a null hypothesis in written form/ a complete sentence, and evaluate them. State a conclusion in plain English.

Answers (1)
  • DJAndro
    April 4, 2023 в 03:00

    Hypothesis: The machine collection system has increased the mean number of cars passing through the toll plaza compared to the human collection system.

    Null Hypothesis: The machine collection system has not increased the mean number of cars passing through the toll plaza compared to the human collection system.

    To evaluate the hypotheses, we can conduct a one-sample t-test. We will use a significance level of 0.05.

    Calculating the t-value:

    t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size)) t = (1261 - 1253) / (59 / sqrt(100)) t = 1.36

    The critical t-value with 99 degrees of freedom at a 0.05 significance level is 1.984. Since the calculated t-value (1.36) is less than the critical t-value (1.984), we fail to reject the null hypothesis.

    Conclusion: There is not enough evidence to suggest that the machine collection system has increased the mean number of cars passing through the toll plaza compared to the human collection system.

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